Unilateral Damage in Reinforced Concrete Frames

Unilateral Damage in Reinforced Concrete Frames

DOI: 10.4018/978-1-4666-6379-4.ch012
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One of the main applications of the lumped damage mechanics or the damage mechanics of dual systems is the earthquake vulnerability assessment of structures. This means not only the consideration of the inertia forces but, mainly, the adequate description of crack propagation under general cyclic loading. Chapter 9 described the concept of unilateral damage (i.e. the appearance of distinct and independent sets of cracks after loading reversals). This phenomenon can also be observed in RC structures, and the models presented in Chapters 10 and 11 do not describe it; thus, they should be used only in the cases of mono sign loadings. The first goal of this chapter is the generalization of the damage models, including unilateral effects; the next one consists of the development of lumped damage models for tridimensional analysis of RC frames. Finally, some guidelines for the use of the damage models in industrial applications are presented.
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12.1 Elasticity Law Under Cyclic Loading

12.1.1 Unilateral Damage in Reinforced Concrete Elements

Figure 1 shows the sequence of cracking patterns in a slender RC specimen subjected to cyclic loading. The two images of the figure show the cracking pattern corresponding to external forces of different sign. It can be observed clearly the two distinct set of cracks.

Figure 1.

a) Cracking pattern in a slender frame element under negative lateral forces b) Cracking pattern after load reversal

Figure 2 shows the same phenomenon in a wall, the two sets of shear cracks can also be appreciated.

Figure 2.

a) Shear cracks under positive, nil and negative lateral forces b) Shear cracks after of several cyclic loads

These damage mechanisms can be characterized using unilateral damage arrays as in continuum damage mechanics (see section 9.2.6): , and , ; the damage parameters and represent crack density due to positive bending moments. The variable measures shear cracking caused by positive shear forces. The damage parameters , and represent, respectively, damage at plastic hinge i due to negative bending moments, flexure negative cracks lumped at plastic hinges j and shear crack density caused by negative shear forces (see Figure 3).

Figure 3.

Unilateral damage in a RC frame element of any aspect ratio under a) positive actions b) negative actions

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